When they won't show work in math?

[lindsey]

Eek. This has been a continual problem with my 3rd grader (BA 3C now). He just does it all in his head. If I insist he show his work he scratches a couple of things down, but ultimately does the calculations in his head. This is proving to be a real problem in the long division section, because the problems will only get trickier and he needs to know the process they are mapping out! I can't even figure out how he's solving some of them in his head. We have MM 3 too, I think (I bought some big printable pack but haven't explored it too much), so I'm going to pull that out tomorrow, but ugh. Anyone else have this problem? He does need to show his work, right?! For the future/harder problems/algebra? 

 

ETA: And MM shows a different way than BA, so now I'm not sure which to show him. Does it ultimately not matter, as long as he can solve it? 

Edited January 5, 2017 by lindsey

[Ellie]

Eek. This has been a continual problem with my 3rd grader (BA 3C now). He just does it all in his head. If I insist he show his work he scratches a couple of things down, but ultimately does the calculations in his head. This is proving to be a real problem in the long division section, because the problems will only get trickier and he needs to know the process they are mapping out! I can't even figure out how he's solving some of them in his head. We have MM 3 too, I think (I bought some big printable pack but haven't explored it too much), so I'm going to pull that out tomorrow, but ugh. Anyone else have this problem? He does need to show his work, right?! For the future/harder problems/algebra? 

 

ETA: And MM shows a different way than BA, so now I'm not sure which to show him. Does it ultimately not matter, as long as he can solve it? 

 

It's pretty common. You have to remain firm, because yes, he does need to show his work.

 

He should show his work according to whichever math method he's doing. Are you *sure* you need to add MM to the mix? If the two methods are different, wouldn't it be better to stick to one or the other?

Edited January 5, 2017 by Ellie

[Guest]

I would teach him as many ways as possible to do every kind of problem, and talk about when one might be preferable over others.

 

As to showing work, I tell my kids to show me once, then talk through out loud any other ways they might know how to solve, and then let them do the rest however they like, including mentally. Any that are incorrect must be worked out longhand in front of me so that I can interrupt him doing it wrong twice, if need be, to avoid creating a "wrong" memory.

 

Imo outside of a test "work" serves solving a problem, it isn't its own problem. As long as we've established that he does know how to do it, however many ways, then not showing work is not a problem for me. Making him write out missed problems encourages him to think ahead "if there's any chance this isn't correct, I might as well work it longhand in the first place."

[SKL]

I have told my kid over and over that she needs to "communicate" with her math teacher.  Knowing something is meaningless in school if you can't / won't communicate it.

 

She sometimes struggles with knowing which things need to be written out, so when that happens, we go over the book's examples and however many other examples are necessary for her to get comfortable.

 

I can relate, because I always found it faster and more efficient to just do the work mentally and write the final answer.  I recall getting a zero on an algebra test because my teacher didn't accept that.  :P  Writing out "step one, step two ..." seemed so stupid at the time.  So yes, I sympathize, but yes, you still have to communicate your method on the paper.  :)  My kid's homework isn't done until the method is communicated.  If that means doing it over a couple times, so be it.  She finally got sick of re-doing and started doing it more or less properly the first time.

 

I will note that this same kid loathes writing.  Apparently it's harder for some people to put their ideas on paper.  My other kid isn't as smart but she is 10x better about showing her work.

[EKS]

If the problems are so easy that he is doing them in his head (and he is getting them right), then, in my heretical opinion, he does not need to show his work.  What he needs are problems that he can't do in his head.  

 

There are a few reasons showing work is necessary, especially in algebra and beyond.  The first is that in math frequently it is not just about getting an "answer" but the process involved in getting that answer.  Sometimes it is *only* about process.  So that's one reason kids need to eventually learn how to write out work.  

 

Another reason is because, eventually, the problems should get hard enough that most students won't be able to hold all of the pieces in mind.  So writing things out is an aid to working memory, and the more legibly, logically, and completely the student writes things out, the easier it will be for him to guard against errors and to find errors when they occur.

 

Yet another reason is that most instructors of algebra and beyond courses will give partial credit and they can't do that if a student hasn't written out the work.  It helps that algebra is where grades start to count for high school.

 

My opinion is that instead of insisting that students show work for trivial computational problems, it is better to get them to a point in their math education where they need to show the work for the reasons I listed above.  But I think that having kids show their work for the sake of showing work is disingenuous and kids can sense that.

Edited January 5, 2017 by EKS

[Lang Syne Boardie]

Agreeing with EKS.

 

Also, when I need to see mastery of a skill (whether math algorithm, Latin declension, sentence diagramming, or anything else), we do it together through recitations and blackboard work. I'd rather watch and listen as he demonstrates in real time than go back and nag over how he did his independent homework. It's not that I don't care, but that I'd rather say, "OK, go to the board and show me," than "Go back and redo these problems, and then turn it in again."

[justasque]

If the problems are so easy that he is doing them in his head (and he is getting them right), then, in my heretical opinion, he does not need to show his work.  What he needs are problems that he can't do in his head.  

...

 

 

I explain that often the text, when teaching a new technique, uses easy problems the student can already solve another way, or even "in their head".  This is done on purpose, because with an easy problem it's more likely that they can "see" how and why the new method works.  However, often the new method can be used on problems that are more complex - ones the old method won't work on.  They need to solve the problem in the specified way, or they miss out on what the author is trying to show them about how the new method and they miss the opportunity to practice the new method with easy problems before tackling harder ones.

 

So yes, it's good to discuss various options as to how to solve a particular problem, and maybe even do two methods and compare the answers, but be careful not to miss out on the specific technique the text is trying to teach.

 

 

[lindsey]

The MM pages I printed were double digit divided by single digit, so those went fine. BA was having him write out 10 + 6 times or whatever, as the quotient. And there's no space to write in the book, which is partly why he does it in his head--he really opposes to writing on a separate piece of paper, for some reason?! I will just keep hassling him. We had a random algebra lesson this past weekend (it came up in a logic puzzles book) and we tried to tie that into why we insist he at least sometimes show his work in math...because some day he will really need to! 

 

 

[scbusf]

College math teacher here - I agree with EKS!!!

[SKL]

I answered the way I did because this child is 8.5 if I understand correctly.  My kids by age 9 were doing a level of math in b&m school that justifies showing work, because it's multi-step and needs to be done in a certain order.  My bright kid who doesn't like to show work has a tendency to make silly mistakes, meaning her ultimate answer is often a nonsense answer if work is not shown.  The teacher can't teach if he can't see where the child went wrong.  I understand that having the student re-do it on a whiteboard is an option, but even that requires that the child know how to show work.  And beginning algebra isn't far in the future at this point.

 

I would agree that showing work for really simple problems is silly.  I remember when my kids were asked to "show their work" on 2nd grade common core worksheets where "showing work" meant drawing 3 rows of 5 stars.  I was impressed that my kids could come up with answers for that sometimes.  :)

[wapiti]

Also agreeing w/EKS.  I have a kid who was like this around that age.  I remember when he was doing AoPS Prealgebra, he'd just shout out the answer after a pause of several minutes and I had to check on the location of the solution manual to make sure he wasn't cheating LOL.  Even now, if he could get away with it, he would probably avoid showing work (handwriting issues).  When he got to systems of equations in algebra, it was finally just too much, and he'd have to write it down.  He is now in algebra 2 at school, where obviously he has to show work, and it is not an issue.

 

I would want to make sure the child knows how to write it out properly, e.g. for long division and multi-digit multiplication, and when the time comes, for basic algebra.  But if the answers are correct most of the time, I wouldn't worry; showing work does not need to be required extensively now in order to be able to do it in the future.  When the time finally comes where showing work is absolutely necessary to solving the problem, the student will have no choice.

 

I also think there are can be significant mental math benefits to doing so much in one's head, great for number sense.

 

Keep a white board and fresh dry erase markers nearby to encourage scratch work.

[LMD]

I explain that often the text, when teaching a new technique, uses easy problems the student can already solve another way, or even "in their head". This is done on purpose, because with an easy problem it's more likely that they can "see" how and why the new method works. However, often the new method can be used on problems that are more complex - ones the old method won't work on. They need to solve the problem in the specified way, or they miss out on what the author is trying to show them about how the new method and they miss the opportunity to practice the new method with easy problems before tackling harder ones.

 

So yes, it's good to discuss various options as to how to solve a particular problem, and maybe even do two methods and compare the answers, but be careful not to miss out on the specific technique the text is trying to teach.

 

 

I agree. Which technique are we talking about here?

 

I explain that these questions aren't testing the math that we both know that they know - I wouldn't make him do questions that are too easy just for fun. So what is the point?

The point is to practice the procedure so that when the question is too difficult for immediate mental maths they have the tools to solve it. We practice the tools with easy problems first so you can see how it works. I almost always demonstrate the steps first with concrete manipulatives, then with drawn symbols, then by repeatedly writing each step myself.

 

It's a variation of working things out multiple ways to cement number sense.

 

And yes, I have stood over them reminding them of every step. My children like to cut corners and then they forget about that ten they regrouped, so I make them redo it and they get a lecture about how showing each step neatly will become very important when they write multiple page proofs later!

It's also important so that you can find where you made an error.

[Mom23Boys]

My oldest is extremely resistant to showing his work. It eventually became a battle of wills, but one I was willing to stick out and win. As math gets harder, with more steps, it's harder to do in your head without messing up numbers. This was a hill I was willing to die on.

 

So I sat him down and calmly explained why he needed to show his work, including things like the joys of partial credit. Mostly though, I stressed that if he didn't get a problem right, and he didn't show his work, I had no idea where the issue was. Did he understand the process and just switch 2 numbers? Did he know how to do the 1st two steps, but not the 3rd? Was he lost on the first step, which made the rest of the problem wrong, even if calculations were correct? Etc.

 

After that, for his daily work, if he did not show his work, he had to go back and redo the problem, even if he got it right. He basically had to do his math 2 times each day for maybe a week. After that, he was consistently showing his work. He was slacking before Christmas break, so I'm going to crack down Monday when we start back.

 

(Our first semester was terrible. We live in Louisiana and our house flooded 8/13 in the major flood in the Baton Rouge area. We live in the hardest hit area. We lived with my BIL and his family for ~12 weeks, all in one room. Public schools have been terribly screwed up too, so there wasn't a good option for this semester. I relaxed a lot bc everyone has been dealing with trauma and loss.)

 

Also, I started giving partial credit on tests. That also motivated him.

[Alice]

My oldest was like this. Very good at Math, did a lot mentally and didn't like to show his work. 

 

Mostly, I didn't make him. If there was a long word problem where he had just written down an answer I would ask him to tell me how he did it. If he could tell me orally I figured that was also communication. If he could not tell me how he did it, we went over it until he was able to explain it and I made sure he understood the concepts. He hated writing and I didn't want to fight the writing battle in math. I also didn't want to limit his math by forcing him to write, which would have slowed him down. 

 

We also use a program that emphasizes mental math (Singapore) so that might have influenced our approach. 

 

For things like long division, I had him do a few problems writing out every step to make sure he got it. Then I would let him do it however he wanted. 

 

As he got older and got more multi-step problems I would make him re-do anything he got wrong. If he just wrote an answer that meant he had to redo the whole thing. If he wrote out his work and I could see where he made the mistake I would show him, or I would tell him to redo from that step on. He quickly realized that it benefited him to show work so that he didn't always have to go back to the beginning. I do the same thing if it's illegible or just messy and I can't follow it. I won't spend a lot of time trying to figure it out but if it's all there neatly, I will help figure out mistakes. 

 

It's worked fine for us. In my experience, it was easy for him to see the point when he needed to start showing work. I emphasized it in Pre-Algebra and Algebra but it wasn't hard to make that transition. It was obvious to him why it was needed. 

 

[rainbowmama]

I insist on problems my nine year old in Beast gets wrong that I see step-by-step work. Anything she gets right I ignore (mostly, though I do make occasional pointed comments about how she should write it all down step-by-step all the time as it reduces careless errors).

[Arcadia]

I'll ask why. My oldest thought it was too easy to write down and his right hand does hurt not just for writing. So we work around that by doing some verbally. My younger one does not have a weak right hand but he just thought it was silly since he could hold everything in his head even simultaneous equations. He is also environmentally friendly and would come after us for wasting paper. He has a boogie board now so environmental problem solved.

 

Boogie board link https://www.amazon.com/Boogie-Board-eWriter-Blue-J32220001/dp/B010HWCEAO

 

Even now, if he could get away with it, he would probably avoid showing work (handwriting issues).

...

When the time finally comes where showing work is absolutely necessary to solving the problem, the student will have no choice.

...

Keep a white board and fresh dry erase markers nearby to encourage scratch work.

Same issue with writing except it was arm/wrist strength for DS12. Still is an issue when writing so he types.

 

I agree. When they have to write the steps whether it is to earn all the points in their math tests or because they can't keep it in their head, they will show their work,

 

My kids did not like even the unscented markers so they learn Latex typing very fast.

[SamanthaCarter]

Ugh. I wish I knew how. I have a ten year old who is doing all his pre-algebra in his head and writing only the answer. He HATES to write. I was overjoyed today when one of his answers was showing work (without my asking). I have told him and shown him that he can solve complicated questions faster on paper because he doesn't have to hold all the pieces in his head. I have gone though periods of not accepting a list of answers, but we keep coming back to that. 

[daijobu]

My kids are allowed to do it in their head if they get the right answer.  

 

I have seen some pretty amazing kids in MathCounts who can do fairly complicated multi-step calculations in their head at lightning speed.  This is a useful skill to have, and it can demonstrate deep insight...if they get the right answer.  

[Farrar]

I wish now that I hadn't fought this battle so much when my kids were younger. I did finally give up, which turned out to be good, because once they got to a certain level with math (pre-algbera), it suddenly wasn't a battle at all. Or, not much of one most of the time. Suddenly the whole idea of showing the work got way easier. So I'm convinced that it's sort of a developmental thing for a lot of kids.

 

I think there are a couple of pieces. There's the problem being so easy they can do it mentally. And there's struggling to get the format of writing out the work. Ds couldn't always get the whole answer in his head, but there would be three steps (or something) and he'd be able to do some in his head and the one that he couldn't (a long multiplication or something), he'd scrawl on the side of the page. And he could not, for the life of him, figure out how to express the whole thing. He could orally explain it though. It was just... executive functioning to some extent, I think. And then he matured enough that he could organize his answers. Today I was just complimenting him on how nice his math page looked, all the steps to the solution shown, the solution given at the bottom.

[Julie of KY]

There are several issues that interplay with showing your work in math and I agree with the points EKS made.

 

From the standpoint of a mom of a very talented math kid with learning disabilities, I vote minimal showing of work in SOME cases. My oldest is currently doing multivariable calculus at home and does the vast majority in his head. For years we've been doing math orally with him spitting out an answer while I scribble away at paper to see if he's correct. :closedeyes:

 

My son had to learn to show work for a few reasons.

• He has to be able to explain the logic of the problem. This was a very different thinking process for him in middle school as usually he could just "see" the answer and it was hard to break it down into steps. Due to severe dysgraphia, we still did this orally for many years with him telling me what to scribe. Most of the problems I'd just let him answer.
• When problems get too complicated to do in your head, then you need to write down some things so that you don't make silly mistakes. This is with very different levels of problems depending on the child. As I said, my oldest does most (hard) calculus problems in his head with no writing.
• For my son (with learning disabilities), learning to WRITE out a problem was essentially a different subject than teaching how to solve the problem. In reality, the first problems he ever wrote out were multi-page math proofs. I know this isn't the norm, but you have to deal with each as an individual.
• It is important to learn how to write out the basic logic steps so that someone else can follow your logic. This becomes very important when turning in work for higher level math/science and might get you partial credit even for the wrong answer.

 

I'd ask WHY you need a student to show work. If they are making silly mistakes, then stepping through work on paper "might" help. If it's just to check the logic, then you might ask for the process on occasion, but then let the student do it in their head if getting the correct answer. Learning HOW to show work in a logical manner is hard for many students and takes time as well.

 

 

[Junie]

My oldest was like this. Very good at Math, did a lot mentally and didn't like to show his work. 

 

Mostly, I didn't make him. If there was a long word problem where he had just written down an answer I would ask him to tell me how he did it. If he could tell me orally I figured that was also communication. If he could not tell me how he did it, we went over it until he was able to explain it and I made sure he understood the concepts. He hated writing and I didn't want to fight the writing battle in math. I also didn't want to limit his math by forcing him to write, which would have slowed him down. 

 

We also use a program that emphasizes mental math (Singapore) so that might have influenced our approach. 

 

For things like long division, I had him do a few problems writing out every step to make sure he got it. Then I would let him do it however he wanted. 

 

As he got older and got more multi-step problems I would make him re-do anything he got wrong. If he just wrote an answer that meant he had to redo the whole thing. If he wrote out his work and I could see where he made the mistake I would show him, or I would tell him to redo from that step on. He quickly realized that it benefited him to show work so that he didn't always have to go back to the beginning. I do the same thing if it's illegible or just messy and I can't follow it. I won't spend a lot of time trying to figure it out but if it's all there neatly, I will help figure out mistakes. 

 

It's worked fine for us. In my experience, it was easy for him to see the point when he needed to start showing work. I emphasized it in Pre-Algebra and Algebra but it wasn't hard to make that transition. It was obvious to him why it was needed. 

 

This sounds like my oldest as well.  He does a lot of math in his head.  When I tried to require him to write down his work he literally couldn't.  I think he understands math in a different way than I do.  I like a very systematic approach.  Write down every baby step.  My dd12 is like this.

 

Ds16, though, is a very visual learner.  He sees things in his head that don't translate to paper easily.  He has tried to explain it to me, but his reasoning really doesn't even make sense to me.  He will often stare off into space, make sounds and wiggle his fingers and then write down an answer.

 

He has learned to write down some of his work now that he is in algebra.  And I give partial credit on tests (although he hates this -- he says it is cheating.  If he got the wrong answer, then he says he shouldn't get any points.)  He also doesn't like to waste paper.

 

Sigh.

[JanetC]

I generally agree with, "If he can do it in his head, he may need harder math. He will show his work when the work is too hard to do in his head."

 

You might also ask yourself if your insistence on showing work has become a challenge to him? You don't want math to become a power struggle.

 

If you criticize any math work that isn't shown in exactly a certain way, you incentivize doing things in your head. When he shows any work, be positive about it. Make only one small correction to it at a time, don't give a long list of all the ways he could have done it better. Show a lot of patience so it doesn't become a battlefield.

[Sarahtar]

Just my 2 cents. My DS was similar. Always does it in his head, or using the calculator (older) but without needing to write anything down. And I always let him do that, because he was getting the right answers. This year - 7th/pre-algebra - suddenly he's not always getting the answers right, and part of it is that the work is just too complex to keep straight in his head, and part of it is that sometimes he makes a small error somewhere and that gets compounded as he completes the problem. He gets to the end, has an answer that he knows isn't the right one/doesn't make sense, and yet he has no way to determine where he went wrong. Writing out his work would allow him to double check his answers more easily. And yet he doesn't.

 

We've quickly reached a place where his NOT writing out the work has made his math take longer than it needs to. It also makes it harder, and more frustrating. He was NOT figuring out from experience that simply taking the time to write down his work would ultimately save time in the long run. So the expectation at this point is that he WILL show his work, even if he just jots down a few of the intermediate steps he took. He needs to write down enough to be able to either tell me what he did to solve the problem OR to be able to look back and verify that all of his calculations are correct. If no work at all is shown, that problem is marked as incorrect and he is expected to re-do it.

[freelylearned]

My son liked to work out math in his head, too at that age, so we worked out a deal that works with both of us. I let him do what he wants in his head, but he has to show me his answers every couple of problems. That way he can't get too far with mistakes because I have him redo the ones he missed and if he redoes them he has to show his work.

 

To help him see the value of graph paper, I also work out sample problems on graph paper at the beginning of every lesson so he can see how helpful it is when used correctly.

 

We also get the Singapore Mental Math books to work through so he learns mental math strategies correctly.

[busymotherof4]

I have a child who can do very complex problems in his head. Even when doing AOPS I would just see some very small amount of chicken scratching and hard to find answers. He ended us switching to a charter school and has learned to show his work and to clearly mark answers in college Algebra. He lost credit on simple silly things at the beginning but wanting an A was the motivation it took. I totally stayed out of it. I'm glad that I didn't fight harder with him at home and let someone else teach that lesson.

[JanetC]

When they start doing "chicken scratching" is when I start teaching showing your work.

Sometimes it's very simple handwriting things, like making sure I can tell the difference between a 2 and a 5. Then moving on to labeling each set of scratchings in a minimal way ("length of side C", "average velocity of train", etc.)

 

Some textbooks and answer keys are overly verbose on what to show, I'm just aiming to ensure my kid gets credit for the work she's doing in her classes with outside teachers. She doesn't have to make her homework look like a textbook chapter, it just needs to be decipherable.

[vonfirmath]

I have told my kid over and over that she needs to "communicate" with her math teacher.  Knowing something is meaningless in school if you can't / won't communicate it.

 

She sometimes struggles with knowing which things need to be written out, so when that happens, we go over the book's examples and however many other examples are necessary for her to get comfortable.

 

I can relate, because I always found it faster and more efficient to just do the work mentally and write the final answer.  I recall getting a zero on an algebra test because my teacher didn't accept that.  :p  Writing out "step one, step two ..." seemed so stupid at the time.  So yes, I sympathize, but yes, you still have to communicate your method on the paper.  :)  My kid's homework isn't done until the method is communicated.  If that means doing it over a couple times, so be it.  She finally got sick of re-doing and started doing it more or less properly the first time.

 

I will note that this same kid loathes writing.  Apparently it's harder for some people to put their ideas on paper.  My other kid isn't as smart but she is 10x better about showing her work.

 

This sounds like my son. He HATES writing -- knows he needs to get better at it and is willing to work at it. But he really dislikes it. So he takes every shortcut he can to not write more than necessary

 

 

I answered the way I did because this child is 8.5 if I understand correctly.  My kids by age 9 were doing a level of math in b&m school that justifies showing work, because it's multi-step and needs to be done in a certain order.  My bright kid who doesn't like to show work has a tendency to make silly mistakes, meaning her ultimate answer is often a nonsense answer if work is not shown.  The teacher can't teach if he can't see where the child went wrong.  I understand that having the student re-do it on a whiteboard is an option, but even that requires that the child know how to show work.  And beginning algebra isn't far in the future at this point.

 

This is also my son.  Things like sometimes writing down "3" in the middle of multi-digit multiplication for 2x1! (I'm also trying to teach him to CHECK his work. He can get as much as half the problems wrong on homework just because he rushes through and makes mistakes like this -- or can't read what he did write down. The numbers all squashed together and forgets to add back in a carried number)  in Multiplication drills where it is JUST multiplication, he regularly makes 100%. These errors creep in when he's doing several steps at once in the space provided (instead of spreading out on another piece of paper)

 

 

Edited January 10, 2017 by vonfirmath

[redsquirrel]

It's difficult. I know that in BA they often encourage problems to be solved without doing any writing. Sometimes it says "See if you can solve this without writing it down," It doesn't exactly bolster my case that he needs to write it down, lol

 

My compromise is that if he gets a problem incorrect then he must do it again while writing it out. And there are problems coming in BA that will require him to write them out, so don't worry that he will never have the chance.  

[KAM]

My rule is I don't care about them showing work except for their quizzes/tests. For everyday lessons if they can do it in their head and get the right answer, great, but otherwise they use scrap paper or a whiteboard as needed and I don't worry too much about it as long as they can figure out how to do it. On days when they have a quiz, I do make them show their work neatly, even for those problems they can do in their head. 

[JanetC]

My rule is I don't care about them showing work except for their quizzes/tests.

If you a actually have to teach the skill of (or debate the merits of) showing work, it doesn't make sense to wait until the test. I gave feedback a step at a time over multiple assignments.

 

Ironically, after going over problems and showing work in everyday practice, I gave full credit for correct answers on tests regardless of how work was shown. So, pretty much the opposite of what you're saying.

 

Reminds me of how hard it is to tell when learning happens despite our teaching methods versus because of them!

[kiwik]

I'll ask why. My oldest thought it was too easy to write down and his right hand does hurt not just for writing. So we work around that by doing some verbally. My younger one does not have a weak right hand but he just thought it was silly since he could hold everything in his head even simultaneous equations. He is also environmentally friendly and would come after us for wasting paper. He has a boogie board now so environmental problem solved.

 

Boogie board link https://www.amazon.com/Boogie-Board-eWriter-Blue-J32220001/dp/B010HWCEAO

 

 

Same issue with writing except it was arm/wrist strength for DS12. Still is an issue when writing so he types.

 

I agree. When they have to write the steps whether it is to earn all the points in their math tests or because they can't keep it in their head, they will show their work,

 

My kids did not like even the unscented markers so they learn Latex typing very fast.

 

Can the notes from the boogie board get transferred to a PC?

[Spy Car]

I was very "mean" that way, requiring either oral explanations of the reasoning (especially in earlier years) or the ordered steps  (sometimes asking for the mathematical properties) that led to the solution.

 

Did my kid like this any more than the typical boy-boy? Nope.

 

But now, as a 12-year-old doing fairly advanced algebra in an advanced math academy (where not showing one's work isn't an option) I think he's seeing the practice pay off. And the complexity of problem sets will only grow.

 

Understanding the operations is what's critical. Being able to explain them (via showing work) promotes mastery.

 

Bill

[Cake and Pi]

My DS#1 hates to write anything at all.  Last year he cried when I asked him to draw a rectangle.  Seriously.   He has almost no work shown for BA 3 and BA 4 (yes, even for long division).  Now in BA 5, he still does most of it in his head, but sometimes he HAS to write some of it out.  The problems, especially those that are multi-step and require the use of variables, are becoming too much for him to hold all the pieces in his head.  I worried a lot about showing work before, but I'm glad now that I didn't push it because he is "discovering" the value of written work on his own.  It's not a battle.  I demonstrate the example problems on the board, modeling correctly shown work, and this has been enough for him.